1. **State the problem:** We are given a piecewise function: $$y=\begin{cases}2 & \text{for } -2 \leq x \leq 0 \\ x^2 & \text{for } 0 < x \leq 2\end{cases}$$ We need to sketch its graph and find its domain and range. 2. **Domain:** The domain is the set of all $x$ values for which the function is defined. From the problem, $x$ ranges from $-2$ to $2$, including $-2$ and $0$ in the first piece, and from just greater than $0$ to $2$ in the second piece. So, domain is: $$[-2,2]$$ 3. **Range:** - For $-2 \leq x \leq 0$, $y=2$ is constant. - For $0 < x \leq 2$, $y=x^2$ which ranges from just above $0^2=0$ to $2^2=4$. Thus, the range is: $$[0,4] \cup \{2\} = [0,4]$$ (since $2$ is already included in $[0,4]$) 4. **Sketching the graph:** - From $x=-2$ to $x=0$, draw a horizontal line at $y=2$. - At $x=0$, the function value is $2$ (from the first piece). - For $x$ just greater than $0$ to $2$, plot $y=x^2$, a parabola segment starting just above $0$ and going up to $4$ at $x=2$. 5. **Summary:** - Domain: $$[-2,2]$$ - Range: $$[0,4]$$ This completes the solution.